************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2013 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be *
* useful, but WITHOUT ANY WARRANTY; without even the implied *
* warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
************************************************************************
------------------------------------------------------------------------
Map identifier: Mp00321
------------------------------------------------------------------------
Map name: 2-conjugate
------------------------------------------------------------------------
Domain: Integer partitions
------------------------------------------------------------------------
Codomain: Integer partitions
------------------------------------------------------------------------
Description: Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def reduction(la, s):
return Partition([p // s for p in la])
def blow_up(nu, s):
return Partition([s * p for p in nu])
def remainder_sequence(la, s):
"""
The sequence of non-zero remainders.
EXAMPLES::
sage: remainder_sequence(Partition([19,16,14,12,7,5,4,3]), 3)
(1, 1, 2, 1, 2, 1)
"""
return tuple(r for p in la if (r := p % s))
def row_sequence(la, s):
"""
The 0-based indices of the parts with non-zero remainder.
EXAMPLES::
sage: row_sequence(Partition([19,16,14,12,7,5,4,3]), 3)
(0, 1, 2, 4, 5, 6)
"""
return tuple(i for i, p in enumerate(la) if p % s)
def green_yellow(la, s):
rho = remainder_sequence(la, s)
gamma = row_sequence(la, s)
return tuple((gamma[j], 0) if (j > 0
and rho[j-1] >= rho[j]
and gamma[j] == gamma[j-1] + 1)
else (gamma[j], 1)
for j in range(len(rho)))
def remainder_diagram(la, s):
return reduction(la, s), green_yellow(la, s)
def conjugate_remainder_diagram(nu, gy):
nu_t = nu.conjugate()
nu = list(nu) + [0]*(gy[-1][0]+1 if gy else 0)
gy_t = [(nu[j], 1) for j, _ in reversed(gy)]
return nu_t, gy_t
def from_remainder_diagram(rho, nu, gy, s):
mu = list(blow_up(nu, s)) + [0]*(gy[-1][0]+1 if gy else 0)
for i, (j, _) in enumerate(gy):
mu[j] += rho[i]
return Partition(mu)
def construction3(rho, nu, gy, verbose=False):
nu = list(nu) + [0]*(gy[-1][0] if gy else 0)
gy = list(gy)
for k in range(len(rho)-1):
if rho[k] < rho[k+1]:
continue
if gy[k+1][1] == 0:
# yellow
for j in range(k, -1, -1):
i = gy[j][0]
nu[i] += 1
gy[j+1] = (i + 1, 1)
gy[0] = (0, 1)
else:
# green
for j in range(k+1):
i = gy[j][0]
nu[i] += 1
gy[j] = (i + 1, 1)
return Partition(nu), tuple(gy)
def construction3_inverse(rho, nu, gy):
nu = list(nu)
gy = list(gy)
for k in range(len(rho)-2, -1, -1):
if rho[k] < rho[k+1]:
continue
if gy[0][0] == 0:
# yellow
for j in range(k+1):
gy[j] = (gy[j+1][0] - 1, 1)
nu[gy[j][0]] -= 1
gy[k+1] = (gy[k+1][0], 0)
else:
# green
for j in range(k+1):
gy[j] = (gy[j][0] - 1, 1)
nu[gy[j][0]] -= 1
return Partition(nu), tuple(gy)
def mapping(la, s=2):
rho = remainder_sequence(la, s)
nu, gy = remainder_diagram(la, s)
nu1, gy1 = construction3(rho, nu, gy)
nu2, gy2 = conjugate_remainder_diagram(nu1, gy1)
nu3, gy3 = construction3_inverse(rho, nu2, gy2)
return from_remainder_diagram(rho, nu3, gy3, s)
------------------------------------------------------------------------
Map images:
[1] => [1]
[2] => [2]
[1,1] => [1,1]
[3] => [2,1]
[2,1] => [3]
[1,1,1] => [1,1,1]
[4] => [2,2]
[3,1] => [2,1,1]
[2,2] => [4]
[2,1,1] => [3,1]
[1,1,1,1] => [1,1,1,1]
[5] => [2,2,1]
[4,1] => [3,2]
[3,2] => [4,1]
[3,1,1] => [2,1,1,1]
[2,2,1] => [5]
[2,1,1,1] => [3,1,1]
[1,1,1,1,1] => [1,1,1,1,1]
[6] => [2,2,2]
[5,1] => [2,2,1,1]
[4,2] => [4,2]
[4,1,1] => [4,1,1]
[3,3] => [3,2,1]
[3,2,1] => [3,3]
[3,1,1,1] => [2,1,1,1,1]
[2,2,2] => [6]
[2,2,1,1] => [5,1]
[2,1,1,1,1] => [3,1,1,1]
[1,1,1,1,1,1] => [1,1,1,1,1,1]
[7] => [2,2,2,1]
[6,1] => [3,2,2]
[5,2] => [4,2,1]
[5,1,1] => [2,2,1,1,1]
[4,3] => [4,3]
[4,2,1] => [5,2]
[4,1,1,1] => [4,1,1,1]
[3,3,1] => [3,2,1,1]
[3,2,2] => [6,1]
[3,2,1,1] => [3,3,1]
[3,1,1,1,1] => [2,1,1,1,1,1]
[2,2,2,1] => [7]
[2,2,1,1,1] => [5,1,1]
[2,1,1,1,1,1] => [3,1,1,1,1]
[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1]
[8] => [2,2,2,2]
[7,1] => [2,2,2,1,1]
[6,2] => [4,2,2]
[6,1,1] => [4,2,1,1]
[5,3] => [3,2,2,1]
[5,2,1] => [3,3,2]
[5,1,1,1] => [2,2,1,1,1,1]
[4,4] => [4,4]
[4,3,1] => [4,3,1]
[4,2,2] => [6,2]
[4,2,1,1] => [6,1,1]
[4,1,1,1,1] => [4,1,1,1,1]
[3,3,2] => [5,2,1]
[3,3,1,1] => [3,2,1,1,1]
[3,2,2,1] => [5,3]
[3,2,1,1,1] => [3,3,1,1]
[3,1,1,1,1,1] => [2,1,1,1,1,1,1]
[2,2,2,2] => [8]
[2,2,2,1,1] => [7,1]
[2,2,1,1,1,1] => [5,1,1,1]
[2,1,1,1,1,1,1] => [3,1,1,1,1,1]
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1]
[9] => [2,2,2,2,1]
[8,1] => [3,2,2,2]
[7,2] => [4,2,2,1]
[7,1,1] => [2,2,2,1,1,1]
[6,3] => [4,3,2]
[6,2,1] => [5,2,2]
[6,1,1,1] => [4,2,1,1,1]
[5,4] => [4,4,1]
[5,3,1] => [3,2,2,1,1]
[5,2,2] => [6,2,1]
[5,2,1,1] => [4,3,1,1]
[5,1,1,1,1] => [2,2,1,1,1,1,1]
[4,4,1] => [5,4]
[4,3,2] => [6,3]
[4,3,1,1] => [5,2,1,1]
[4,2,2,1] => [7,2]
[4,2,1,1,1] => [6,1,1,1]
[4,1,1,1,1,1] => [4,1,1,1,1,1]
[3,3,3] => [3,3,2,1]
[3,3,2,1] => [3,3,3]
[3,3,1,1,1] => [3,2,1,1,1,1]
[3,2,2,2] => [8,1]
[3,2,2,1,1] => [5,3,1]
[3,2,1,1,1,1] => [3,3,1,1,1]
[3,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1]
[2,2,2,2,1] => [9]
[2,2,2,1,1,1] => [7,1,1]
[2,2,1,1,1,1,1] => [5,1,1,1,1]
[2,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1]
[10] => [2,2,2,2,2]
[9,1] => [2,2,2,2,1,1]
[8,2] => [4,2,2,2]
[8,1,1] => [4,2,2,1,1]
[7,3] => [3,2,2,2,1]
[7,2,1] => [3,3,2,2]
[7,1,1,1] => [2,2,2,1,1,1,1]
[6,4] => [4,4,2]
[6,3,1] => [4,4,1,1]
[6,2,2] => [6,2,2]
[6,2,1,1] => [6,2,1,1]
[6,1,1,1,1] => [4,2,1,1,1,1]
[5,5] => [4,3,2,1]
[5,4,1] => [4,3,3]
[5,3,2] => [5,2,2,1]
[5,3,1,1] => [3,2,2,1,1,1]
[5,2,2,1] => [5,3,2]
[5,2,1,1,1] => [4,3,1,1,1]
[5,1,1,1,1,1] => [2,2,1,1,1,1,1,1]
[4,4,2] => [6,4]
[4,4,1,1] => [6,3,1]
[4,3,3] => [5,4,1]
[4,3,2,1] => [5,5]
[4,3,1,1,1] => [5,2,1,1,1]
[4,2,2,2] => [8,2]
[4,2,2,1,1] => [8,1,1]
[4,2,1,1,1,1] => [6,1,1,1,1]
[4,1,1,1,1,1,1] => [4,1,1,1,1,1,1]
[3,3,3,1] => [3,3,2,1,1]
[3,3,2,2] => [7,2,1]
[3,3,2,1,1] => [3,3,3,1]
[3,3,1,1,1,1] => [3,2,1,1,1,1,1]
[3,2,2,2,1] => [7,3]
[3,2,2,1,1,1] => [5,3,1,1]
[3,2,1,1,1,1,1] => [3,3,1,1,1,1]
[3,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1]
[2,2,2,2,2] => [10]
[2,2,2,2,1,1] => [9,1]
[2,2,2,1,1,1,1] => [7,1,1,1]
[2,2,1,1,1,1,1,1] => [5,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1]
[11] => [2,2,2,2,2,1]
[10,1] => [3,2,2,2,2]
[9,2] => [4,2,2,2,1]
[9,1,1] => [2,2,2,2,1,1,1]
[8,3] => [4,3,2,2]
[8,2,1] => [5,2,2,2]
[8,1,1,1] => [4,2,2,1,1,1]
[7,4] => [4,4,2,1]
[7,3,1] => [3,2,2,2,1,1]
[7,2,2] => [6,2,2,1]
[7,2,1,1] => [4,4,1,1,1]
[7,1,1,1,1] => [2,2,2,1,1,1,1,1]
[6,5] => [4,4,3]
[6,4,1] => [5,4,2]
[6,3,2] => [6,3,2]
[6,3,1,1] => [5,2,2,1,1]
[6,2,2,1] => [7,2,2]
[6,2,1,1,1] => [6,2,1,1,1]
[6,1,1,1,1,1] => [4,2,1,1,1,1,1]
[5,5,1] => [4,3,2,1,1]
[5,4,2] => [6,4,1]
[5,4,1,1] => [4,3,3,1]
[5,3,3] => [3,3,2,2,1]
[5,3,2,1] => [3,3,3,2]
[5,3,1,1,1] => [3,2,2,1,1,1,1]
[5,2,2,2] => [8,2,1]
[5,2,2,1,1] => [6,3,1,1]
[5,2,1,1,1,1] => [4,3,1,1,1,1]
[5,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1]
[4,4,3] => [6,5]
[4,4,2,1] => [7,4]
[4,4,1,1,1] => [7,2,1,1]
[4,3,3,1] => [5,4,1,1]
[4,3,2,2] => [8,3]
[4,3,2,1,1] => [5,5,1]
[4,3,1,1,1,1] => [5,2,1,1,1,1]
[4,2,2,2,1] => [9,2]
[4,2,2,1,1,1] => [8,1,1,1]
[4,2,1,1,1,1,1] => [6,1,1,1,1,1]
[4,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1]
[3,3,3,2] => [5,3,2,1]
[3,3,3,1,1] => [3,3,2,1,1,1]
[3,3,2,2,1] => [5,3,3]
[3,3,2,1,1,1] => [3,3,3,1,1]
[3,3,1,1,1,1,1] => [3,2,1,1,1,1,1,1]
[3,2,2,2,2] => [10,1]
[3,2,2,2,1,1] => [7,3,1]
[3,2,2,1,1,1,1] => [5,3,1,1,1]
[3,2,1,1,1,1,1,1] => [3,3,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,1] => [11]
[2,2,2,2,1,1,1] => [9,1,1]
[2,2,2,1,1,1,1,1] => [7,1,1,1,1]
[2,2,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1]
[12] => [2,2,2,2,2,2]
[11,1] => [2,2,2,2,2,1,1]
[10,2] => [4,2,2,2,2]
[10,1,1] => [4,2,2,2,1,1]
[9,3] => [3,2,2,2,2,1]
[9,2,1] => [3,3,2,2,2]
[9,1,1,1] => [2,2,2,2,1,1,1,1]
[8,4] => [4,4,2,2]
[8,3,1] => [4,4,2,1,1]
[8,2,2] => [6,2,2,2]
[8,2,1,1] => [6,2,2,1,1]
[8,1,1,1,1] => [4,2,2,1,1,1,1]
[7,5] => [4,3,2,2,1]
[7,4,1] => [4,3,3,2]
[7,3,2] => [5,2,2,2,1]
[7,3,1,1] => [3,2,2,2,1,1,1]
[7,2,2,1] => [5,3,2,2]
[7,2,1,1,1] => [4,4,1,1,1,1]
[7,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1]
[6,6] => [4,4,4]
[6,5,1] => [4,4,3,1]
[6,4,2] => [6,4,2]
[6,4,1,1] => [6,4,1,1]
[6,3,3] => [5,4,2,1]
[6,3,2,1] => [5,5,2]
[6,3,1,1,1] => [5,2,2,1,1,1]
[6,2,2,2] => [8,2,2]
[6,2,2,1,1] => [8,2,1,1]
[6,2,1,1,1,1] => [6,2,1,1,1,1]
[6,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1]
[5,5,2] => [6,3,2,1]
[5,5,1,1] => [4,3,2,1,1,1]
[5,4,3] => [5,4,3]
[5,4,2,1] => [6,3,3]
[5,4,1,1,1] => [5,4,1,1,1]
[5,3,3,1] => [3,3,2,2,1,1]
[5,3,2,2] => [7,2,2,1]
[5,3,2,1,1] => [4,3,3,1,1]
[5,3,1,1,1,1] => [3,2,2,1,1,1,1,1]
[5,2,2,2,1] => [7,3,2]
[5,2,2,1,1,1] => [6,3,1,1,1]
[5,2,1,1,1,1,1] => [4,3,1,1,1,1,1]
[5,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1]
[4,4,4] => [6,6]
[4,4,3,1] => [6,5,1]
[4,4,2,2] => [8,4]
[4,4,2,1,1] => [8,3,1]
[4,4,1,1,1,1] => [7,2,1,1,1]
[4,3,3,2] => [7,4,1]
[4,3,3,1,1] => [5,3,2,1,1]
[4,3,2,2,1] => [7,5]
[4,3,2,1,1,1] => [5,5,1,1]
[4,3,1,1,1,1,1] => [5,2,1,1,1,1,1]
[4,2,2,2,2] => [10,2]
[4,2,2,2,1,1] => [10,1,1]
[4,2,2,1,1,1,1] => [8,1,1,1,1]
[4,2,1,1,1,1,1,1] => [6,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1]
[3,3,3,3] => [3,3,3,2,1]
[3,3,3,2,1] => [3,3,3,3]
[3,3,3,1,1,1] => [3,3,2,1,1,1,1]
[3,3,2,2,2] => [9,2,1]
[3,3,2,2,1,1] => [5,3,3,1]
[3,3,2,1,1,1,1] => [3,3,3,1,1,1]
[3,3,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1]
[3,2,2,2,2,1] => [9,3]
[3,2,2,2,1,1,1] => [7,3,1,1]
[3,2,2,1,1,1,1,1] => [5,3,1,1,1,1]
[3,2,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2] => [12]
[2,2,2,2,2,1,1] => [11,1]
[2,2,2,2,1,1,1,1] => [9,1,1,1]
[2,2,2,1,1,1,1,1,1] => [7,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1]
[13] => [2,2,2,2,2,2,1]
[12,1] => [3,2,2,2,2,2]
[11,2] => [4,2,2,2,2,1]
[11,1,1] => [2,2,2,2,2,1,1,1]
[10,3] => [4,3,2,2,2]
[10,2,1] => [5,2,2,2,2]
[10,1,1,1] => [4,2,2,2,1,1,1]
[9,4] => [4,4,2,2,1]
[9,3,1] => [3,2,2,2,2,1,1]
[9,2,2] => [6,2,2,2,1]
[9,2,1,1] => [4,4,2,1,1,1]
[9,1,1,1,1] => [2,2,2,2,1,1,1,1,1]
[8,5] => [4,4,3,2]
[8,4,1] => [5,4,2,2]
[8,3,2] => [6,3,2,2]
[8,3,1,1] => [5,2,2,2,1,1]
[8,2,2,1] => [7,2,2,2]
[8,2,1,1,1] => [6,2,2,1,1,1]
[8,1,1,1,1,1] => [4,2,2,1,1,1,1,1]
[7,6] => [4,4,4,1]
[7,5,1] => [4,3,2,2,1,1]
[7,4,2] => [6,4,2,1]
[7,4,1,1] => [4,4,3,1,1]
[7,3,3] => [3,3,2,2,2,1]
[7,3,2,1] => [3,3,3,2,2]
[7,3,1,1,1] => [3,2,2,2,1,1,1,1]
[7,2,2,2] => [8,2,2,1]
[7,2,2,1,1] => [6,4,1,1,1]
[7,2,1,1,1,1] => [4,4,1,1,1,1,1]
[7,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1]
[6,6,1] => [5,4,4]
[6,5,2] => [6,4,3]
[6,5,1,1] => [6,3,2,1,1]
[6,4,3] => [6,5,2]
[6,4,2,1] => [7,4,2]
[6,4,1,1,1] => [7,2,2,1,1]
[6,3,3,1] => [5,4,2,1,1]
[6,3,2,2] => [8,3,2]
[6,3,2,1,1] => [6,5,1,1]
[6,3,1,1,1,1] => [5,2,2,1,1,1,1]
[6,2,2,2,1] => [9,2,2]
[6,2,2,1,1,1] => [8,2,1,1,1]
[6,2,1,1,1,1,1] => [6,2,1,1,1,1,1]
[6,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1]
[5,5,3] => [4,3,3,2,1]
[5,5,2,1] => [4,3,3,3]
[5,5,1,1,1] => [4,3,2,1,1,1,1]
[5,4,4] => [6,6,1]
[5,4,3,1] => [5,4,3,1]
[5,4,2,2] => [8,4,1]
[5,4,2,1,1] => [6,3,3,1]
[5,4,1,1,1,1] => [5,4,1,1,1,1]
[5,3,3,2] => [5,3,2,2,1]
[5,3,3,1,1] => [3,3,2,2,1,1,1]
[5,3,2,2,1] => [5,3,3,2]
[5,3,2,1,1,1] => [4,3,3,1,1,1]
[5,3,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1]
[5,2,2,2,2] => [10,2,1]
[5,2,2,2,1,1] => [8,3,1,1]
[5,2,2,1,1,1,1] => [6,3,1,1,1,1]
[5,2,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1]
[4,4,4,1] => [7,6]
[4,4,3,2] => [8,5]
[4,4,3,1,1] => [7,4,1,1]
[4,4,2,2,1] => [9,4]
[4,4,2,1,1,1] => [9,2,1,1]
[4,4,1,1,1,1,1] => [7,2,1,1,1,1]
[4,3,3,3] => [5,5,2,1]
[4,3,3,2,1] => [5,5,3]
[4,3,3,1,1,1] => [5,3,2,1,1,1]
[4,3,2,2,2] => [10,3]
[4,3,2,2,1,1] => [7,5,1]
[4,3,2,1,1,1,1] => [5,5,1,1,1]
[4,3,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1]
[4,2,2,2,2,1] => [11,2]
[4,2,2,2,1,1,1] => [10,1,1,1]
[4,2,2,1,1,1,1,1] => [8,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1]
[3,3,3,3,1] => [3,3,3,2,1,1]
[3,3,3,2,2] => [7,3,2,1]
[3,3,3,2,1,1] => [3,3,3,3,1]
[3,3,3,1,1,1,1] => [3,3,2,1,1,1,1,1]
[3,3,2,2,2,1] => [7,3,3]
[3,3,2,2,1,1,1] => [5,3,3,1,1]
[3,3,2,1,1,1,1,1] => [3,3,3,1,1,1,1]
[3,3,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2] => [12,1]
[3,2,2,2,2,1,1] => [9,3,1]
[3,2,2,2,1,1,1,1] => [7,3,1,1,1]
[3,2,2,1,1,1,1,1,1] => [5,3,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,1] => [13]
[2,2,2,2,2,1,1,1] => [11,1,1]
[2,2,2,2,1,1,1,1,1] => [9,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1]
[14] => [2,2,2,2,2,2,2]
[13,1] => [2,2,2,2,2,2,1,1]
[12,2] => [4,2,2,2,2,2]
[12,1,1] => [4,2,2,2,2,1,1]
[11,3] => [3,2,2,2,2,2,1]
[11,2,1] => [3,3,2,2,2,2]
[11,1,1,1] => [2,2,2,2,2,1,1,1,1]
[10,4] => [4,4,2,2,2]
[10,3,1] => [4,4,2,2,1,1]
[10,2,2] => [6,2,2,2,2]
[10,2,1,1] => [6,2,2,2,1,1]
[10,1,1,1,1] => [4,2,2,2,1,1,1,1]
[9,5] => [4,3,2,2,2,1]
[9,4,1] => [4,3,3,2,2]
[9,3,2] => [5,2,2,2,2,1]
[9,3,1,1] => [3,2,2,2,2,1,1,1]
[9,2,2,1] => [5,3,2,2,2]
[9,2,1,1,1] => [4,4,2,1,1,1,1]
[9,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1]
[8,6] => [4,4,4,2]
[8,5,1] => [4,4,4,1,1]
[8,4,2] => [6,4,2,2]
[8,4,1,1] => [6,4,2,1,1]
[8,3,3] => [5,4,2,2,1]
[8,3,2,1] => [5,5,2,2]
[8,3,1,1,1] => [5,2,2,2,1,1,1]
[8,2,2,2] => [8,2,2,2]
[8,2,2,1,1] => [8,2,2,1,1]
[8,2,1,1,1,1] => [6,2,2,1,1,1,1]
[8,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1]
[7,7] => [4,4,3,2,1]
[7,6,1] => [4,4,3,3]
[7,5,2] => [6,3,2,2,1]
[7,5,1,1] => [4,3,2,2,1,1,1]
[7,4,3] => [5,4,3,2]
[7,4,2,1] => [6,3,3,2]
[7,4,1,1,1] => [5,4,2,1,1,1]
[7,3,3,1] => [3,3,2,2,2,1,1]
[7,3,2,2] => [7,2,2,2,1]
[7,3,2,1,1] => [4,4,3,1,1,1]
[7,3,1,1,1,1] => [3,2,2,2,1,1,1,1,1]
[7,2,2,2,1] => [7,3,2,2]
[7,2,2,1,1,1] => [6,4,1,1,1,1]
[7,2,1,1,1,1,1] => [4,4,1,1,1,1,1,1]
[7,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1]
[6,6,2] => [6,4,4]
[6,6,1,1] => [6,4,3,1]
[6,5,3] => [5,4,4,1]
[6,5,2,1] => [5,5,4]
[6,5,1,1,1] => [6,3,2,1,1,1]
[6,4,4] => [6,6,2]
[6,4,3,1] => [6,6,1,1]
[6,4,2,2] => [8,4,2]
[6,4,2,1,1] => [8,4,1,1]
[6,4,1,1,1,1] => [7,2,2,1,1,1]
[6,3,3,2] => [7,4,2,1]
[6,3,3,1,1] => [5,3,2,2,1,1]
[6,3,2,2,1] => [7,5,2]
[6,3,2,1,1,1] => [6,5,1,1,1]
[6,3,1,1,1,1,1] => [5,2,2,1,1,1,1,1]
[6,2,2,2,2] => [10,2,2]
[6,2,2,2,1,1] => [10,2,1,1]
[6,2,2,1,1,1,1] => [8,2,1,1,1,1]
[6,2,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1]
[6,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1]
[5,5,4] => [6,5,2,1]
[5,5,3,1] => [4,3,3,2,1,1]
[5,5,2,2] => [8,3,2,1]
[5,5,2,1,1] => [4,3,3,3,1]
[5,5,1,1,1,1] => [4,3,2,1,1,1,1,1]
[5,4,4,1] => [6,5,3]
[5,4,3,2] => [7,4,3]
[5,4,3,1,1] => [5,4,3,1,1]
[5,4,2,2,1] => [8,3,3]
[5,4,2,1,1,1] => [7,4,1,1,1]
[5,4,1,1,1,1,1] => [5,4,1,1,1,1,1]
[5,3,3,3] => [3,3,3,2,2,1]
[5,3,3,2,1] => [3,3,3,3,2]
[5,3,3,1,1,1] => [3,3,2,2,1,1,1,1]
[5,3,2,2,2] => [9,2,2,1]
[5,3,2,2,1,1] => [6,3,3,1,1]
[5,3,2,1,1,1,1] => [4,3,3,1,1,1,1]
[5,3,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1]
[5,2,2,2,2,1] => [9,3,2]
[5,2,2,2,1,1,1] => [8,3,1,1,1]
[5,2,2,1,1,1,1,1] => [6,3,1,1,1,1,1]
[5,2,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1]
[4,4,4,2] => [8,6]
[4,4,4,1,1] => [8,5,1]
[4,4,3,3] => [7,6,1]
[4,4,3,2,1] => [7,7]
[4,4,3,1,1,1] => [7,3,2,1,1]
[4,4,2,2,2] => [10,4]
[4,4,2,2,1,1] => [10,3,1]
[4,4,2,1,1,1,1] => [9,2,1,1,1]
[4,4,1,1,1,1,1,1] => [7,2,1,1,1,1,1]
[4,3,3,3,1] => [5,5,2,1,1]
[4,3,3,2,2] => [9,4,1]
[4,3,3,2,1,1] => [5,5,3,1]
[4,3,3,1,1,1,1] => [5,3,2,1,1,1,1]
[4,3,2,2,2,1] => [9,5]
[4,3,2,2,1,1,1] => [7,5,1,1]
[4,3,2,1,1,1,1,1] => [5,5,1,1,1,1]
[4,3,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1]
[4,2,2,2,2,2] => [12,2]
[4,2,2,2,2,1,1] => [12,1,1]
[4,2,2,2,1,1,1,1] => [10,1,1,1,1]
[4,2,2,1,1,1,1,1,1] => [8,1,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1]
[3,3,3,3,2] => [5,3,3,2,1]
[3,3,3,3,1,1] => [3,3,3,2,1,1,1]
[3,3,3,2,2,1] => [5,3,3,3]
[3,3,3,2,1,1,1] => [3,3,3,3,1,1]
[3,3,3,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1]
[3,3,2,2,2,2] => [11,2,1]
[3,3,2,2,2,1,1] => [7,3,3,1]
[3,3,2,2,1,1,1,1] => [5,3,3,1,1,1]
[3,3,2,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2,1] => [11,3]
[3,2,2,2,2,1,1,1] => [9,3,1,1]
[3,2,2,2,1,1,1,1,1] => [7,3,1,1,1,1]
[3,2,2,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,2] => [14]
[2,2,2,2,2,2,1,1] => [13,1]
[2,2,2,2,2,1,1,1,1] => [11,1,1,1]
[2,2,2,2,1,1,1,1,1,1] => [9,1,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[15] => [2,2,2,2,2,2,2,1]
[14,1] => [3,2,2,2,2,2,2]
[13,2] => [4,2,2,2,2,2,1]
[13,1,1] => [2,2,2,2,2,2,1,1,1]
[12,3] => [4,3,2,2,2,2]
[12,2,1] => [5,2,2,2,2,2]
[12,1,1,1] => [4,2,2,2,2,1,1,1]
[11,4] => [4,4,2,2,2,1]
[11,3,1] => [3,2,2,2,2,2,1,1]
[11,2,2] => [6,2,2,2,2,1]
[11,2,1,1] => [4,4,2,2,1,1,1]
[11,1,1,1,1] => [2,2,2,2,2,1,1,1,1,1]
[10,5] => [4,4,3,2,2]
[10,4,1] => [5,4,2,2,2]
[10,3,2] => [6,3,2,2,2]
[10,3,1,1] => [5,2,2,2,2,1,1]
[10,2,2,1] => [7,2,2,2,2]
[10,2,1,1,1] => [6,2,2,2,1,1,1]
[10,1,1,1,1,1] => [4,2,2,2,1,1,1,1,1]
[9,6] => [4,4,4,2,1]
[9,5,1] => [4,3,2,2,2,1,1]
[9,4,2] => [6,4,2,2,1]
[9,4,1,1] => [4,4,4,1,1,1]
[9,3,3] => [3,3,2,2,2,2,1]
[9,3,2,1] => [3,3,3,2,2,2]
[9,3,1,1,1] => [3,2,2,2,2,1,1,1,1]
[9,2,2,2] => [8,2,2,2,1]
[9,2,2,1,1] => [6,4,2,1,1,1]
[9,2,1,1,1,1] => [4,4,2,1,1,1,1,1]
[9,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1,1]
[8,7] => [4,4,4,3]
[8,6,1] => [5,4,4,2]
[8,5,2] => [6,4,3,2]
[8,5,1,1] => [6,3,2,2,1,1]
[8,4,3] => [6,5,2,2]
[8,4,2,1] => [7,4,2,2]
[8,4,1,1,1] => [7,2,2,2,1,1]
[8,3,3,1] => [5,4,2,2,1,1]
[8,3,2,2] => [8,3,2,2]
[8,3,2,1,1] => [6,6,1,1,1]
[8,3,1,1,1,1] => [5,2,2,2,1,1,1,1]
[8,2,2,2,1] => [9,2,2,2]
[8,2,2,1,1,1] => [8,2,2,1,1,1]
[8,2,1,1,1,1,1] => [6,2,2,1,1,1,1,1]
[8,1,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1,1]
[7,7,1] => [4,4,3,2,1,1]
[7,6,2] => [6,4,4,1]
[7,6,1,1] => [4,4,3,3,1]
[7,5,3] => [4,3,3,2,2,1]
[7,5,2,1] => [4,3,3,3,2]
[7,5,1,1,1] => [4,3,2,2,1,1,1,1]
[7,4,4] => [6,6,2,1]
[7,4,3,1] => [5,4,4,1,1]
[7,4,2,2] => [8,4,2,1]
[7,4,2,1,1] => [6,4,3,1,1]
[7,4,1,1,1,1] => [5,4,2,1,1,1,1]
[7,3,3,2] => [5,3,2,2,2,1]
[7,3,3,1,1] => [3,3,2,2,2,1,1,1]
[7,3,2,2,1] => [5,3,3,2,2]
[7,3,2,1,1,1] => [4,4,3,1,1,1,1]
[7,3,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1,1]
[7,2,2,2,2] => [10,2,2,1]
[7,2,2,2,1,1] => [8,4,1,1,1]
[7,2,2,1,1,1,1] => [6,4,1,1,1,1,1]
[7,2,1,1,1,1,1,1] => [4,4,1,1,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1]
[6,6,3] => [6,5,4]
[6,6,2,1] => [7,4,4]
[6,6,1,1,1] => [8,3,2,1,1]
[6,5,4] => [6,6,3]
[6,5,3,1] => [6,5,2,1,1]
[6,5,2,2] => [8,4,3]
[6,5,2,1,1] => [6,5,3,1]
[6,5,1,1,1,1] => [6,3,2,1,1,1,1]
[6,4,4,1] => [7,6,2]
[6,4,3,2] => [8,5,2]
[6,4,3,1,1] => [7,4,2,1,1]
[6,4,2,2,1] => [9,4,2]
[6,4,2,1,1,1] => [9,2,2,1,1]
[6,4,1,1,1,1,1] => [7,2,2,1,1,1,1]
[6,3,3,3] => [5,5,2,2,1]
[6,3,3,2,1] => [5,5,3,2]
[6,3,3,1,1,1] => [5,3,2,2,1,1,1]
[6,3,2,2,2] => [10,3,2]
[6,3,2,2,1,1] => [8,5,1,1]
[6,3,2,1,1,1,1] => [6,5,1,1,1,1]
[6,3,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1]
[6,2,2,2,2,1] => [11,2,2]
[6,2,2,2,1,1,1] => [10,2,1,1,1]
[6,2,2,1,1,1,1,1] => [8,2,1,1,1,1,1]
[6,2,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1]
[5,5,5] => [5,4,3,2,1]
[5,5,4,1] => [5,4,3,3]
[5,5,3,2] => [6,3,3,2,1]
[5,5,3,1,1] => [4,3,3,2,1,1,1]
[5,5,2,2,1] => [6,3,3,3]
[5,5,2,1,1,1] => [5,4,3,1,1,1]
[5,5,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1]
[5,4,4,2] => [8,6,1]
[5,4,4,1,1] => [7,4,3,1]
[5,4,3,3] => [5,5,4,1]
[5,4,3,2,1] => [5,5,5]
[5,4,3,1,1,1] => [5,5,2,1,1,1]
[5,4,2,2,2] => [10,4,1]
[5,4,2,2,1,1] => [8,3,3,1]
[5,4,2,1,1,1,1] => [7,4,1,1,1,1]
[5,4,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1]
[5,3,3,3,1] => [3,3,3,2,2,1,1]
[5,3,3,2,2] => [7,3,2,2,1]
[5,3,3,2,1,1] => [4,3,3,3,1,1]
[5,3,3,1,1,1,1] => [3,3,2,2,1,1,1,1,1]
[5,3,2,2,2,1] => [7,3,3,2]
[5,3,2,2,1,1,1] => [6,3,3,1,1,1]
[5,3,2,1,1,1,1,1] => [4,3,3,1,1,1,1,1]
[5,3,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1,1]
[5,2,2,2,2,2] => [12,2,1]
[5,2,2,2,2,1,1] => [10,3,1,1]
[5,2,2,2,1,1,1,1] => [8,3,1,1,1,1]
[5,2,2,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1]
[5,2,1,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1]
[4,4,4,3] => [8,7]
[4,4,4,2,1] => [9,6]
[4,4,4,1,1,1] => [9,4,1,1]
[4,4,3,3,1] => [7,6,1,1]
[4,4,3,2,2] => [10,5]
[4,4,3,2,1,1] => [7,7,1]
[4,4,3,1,1,1,1] => [7,3,2,1,1,1]
[4,4,2,2,2,1] => [11,4]
[4,4,2,2,1,1,1] => [11,2,1,1]
[4,4,2,1,1,1,1,1] => [9,2,1,1,1,1]
[4,4,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1]
[4,3,3,3,2] => [7,5,2,1]
[4,3,3,3,1,1] => [5,3,3,2,1,1]
[4,3,3,2,2,1] => [7,5,3]
[4,3,3,2,1,1,1] => [5,5,3,1,1]
[4,3,3,1,1,1,1,1] => [5,3,2,1,1,1,1,1]
[4,3,2,2,2,2] => [12,3]
[4,3,2,2,2,1,1] => [9,5,1]
[4,3,2,2,1,1,1,1] => [7,5,1,1,1]
[4,3,2,1,1,1,1,1,1] => [5,5,1,1,1,1,1]
[4,3,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1]
[4,2,2,2,2,2,1] => [13,2]
[4,2,2,2,2,1,1,1] => [12,1,1,1]
[4,2,2,2,1,1,1,1,1] => [10,1,1,1,1,1]
[4,2,2,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1]
[3,3,3,3,3] => [3,3,3,3,2,1]
[3,3,3,3,2,1] => [3,3,3,3,3]
[3,3,3,3,1,1,1] => [3,3,3,2,1,1,1,1]
[3,3,3,2,2,2] => [9,3,2,1]
[3,3,3,2,2,1,1] => [5,3,3,3,1]
[3,3,3,2,1,1,1,1] => [3,3,3,3,1,1,1]
[3,3,3,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1,1]
[3,3,2,2,2,2,1] => [9,3,3]
[3,3,2,2,2,1,1,1] => [7,3,3,1,1]
[3,3,2,2,1,1,1,1,1] => [5,3,3,1,1,1,1]
[3,3,2,1,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2,2] => [14,1]
[3,2,2,2,2,2,1,1] => [11,3,1]
[3,2,2,2,2,1,1,1,1] => [9,3,1,1,1]
[3,2,2,2,1,1,1,1,1,1] => [7,3,1,1,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,2,1] => [15]
[2,2,2,2,2,2,1,1,1] => [13,1,1]
[2,2,2,2,2,1,1,1,1,1] => [11,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[16] => [2,2,2,2,2,2,2,2]
[15,1] => [2,2,2,2,2,2,2,1,1]
[14,2] => [4,2,2,2,2,2,2]
[14,1,1] => [4,2,2,2,2,2,1,1]
[13,3] => [3,2,2,2,2,2,2,1]
[13,2,1] => [3,3,2,2,2,2,2]
[13,1,1,1] => [2,2,2,2,2,2,1,1,1,1]
[12,4] => [4,4,2,2,2,2]
[12,3,1] => [4,4,2,2,2,1,1]
[12,2,2] => [6,2,2,2,2,2]
[12,2,1,1] => [6,2,2,2,2,1,1]
[12,1,1,1,1] => [4,2,2,2,2,1,1,1,1]
[11,5] => [4,3,2,2,2,2,1]
[11,4,1] => [4,3,3,2,2,2]
[11,3,2] => [5,2,2,2,2,2,1]
[11,3,1,1] => [3,2,2,2,2,2,1,1,1]
[11,2,2,1] => [5,3,2,2,2,2]
[11,2,1,1,1] => [4,4,2,2,1,1,1,1]
[11,1,1,1,1,1] => [2,2,2,2,2,1,1,1,1,1,1]
[10,6] => [4,4,4,2,2]
[10,5,1] => [4,4,4,2,1,1]
[10,4,2] => [6,4,2,2,2]
[10,4,1,1] => [6,4,2,2,1,1]
[10,3,3] => [5,4,2,2,2,1]
[10,3,2,1] => [5,5,2,2,2]
[10,3,1,1,1] => [5,2,2,2,2,1,1,1]
[10,2,2,2] => [8,2,2,2,2]
[10,2,2,1,1] => [8,2,2,2,1,1]
[10,2,1,1,1,1] => [6,2,2,2,1,1,1,1]
[10,1,1,1,1,1,1] => [4,2,2,2,1,1,1,1,1,1]
[9,7] => [4,4,3,2,2,1]
[9,6,1] => [4,4,3,3,2]
[9,5,2] => [6,3,2,2,2,1]
[9,5,1,1] => [4,3,2,2,2,1,1,1]
[9,4,3] => [5,4,3,2,2]
[9,4,2,1] => [6,3,3,2,2]
[9,4,1,1,1] => [5,4,2,2,1,1,1]
[9,3,3,1] => [3,3,2,2,2,2,1,1]
[9,3,2,2] => [7,2,2,2,2,1]
[9,3,2,1,1] => [4,4,4,1,1,1,1]
[9,3,1,1,1,1] => [3,2,2,2,2,1,1,1,1,1]
[9,2,2,2,1] => [7,3,2,2,2]
[9,2,2,1,1,1] => [6,4,2,1,1,1,1]
[9,2,1,1,1,1,1] => [4,4,2,1,1,1,1,1,1]
[9,1,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1,1,1]
[8,8] => [4,4,4,4]
[8,7,1] => [4,4,4,3,1]
[8,6,2] => [6,4,4,2]
[8,6,1,1] => [6,4,4,1,1]
[8,5,3] => [5,4,4,2,1]
[8,5,2,1] => [5,5,4,2]
[8,5,1,1,1] => [6,3,2,2,1,1,1]
[8,4,4] => [6,6,2,2]
[8,4,3,1] => [6,6,2,1,1]
[8,4,2,2] => [8,4,2,2]
[8,4,2,1,1] => [8,4,2,1,1]
[8,4,1,1,1,1] => [7,2,2,2,1,1,1]
[8,3,3,2] => [7,4,2,2,1]
[8,3,3,1,1] => [5,3,2,2,2,1,1]
[8,3,2,2,1] => [7,5,2,2]
[8,3,2,1,1,1] => [6,6,1,1,1,1]
[8,3,1,1,1,1,1] => [5,2,2,2,1,1,1,1,1]
[8,2,2,2,2] => [10,2,2,2]
[8,2,2,2,1,1] => [10,2,2,1,1]
[8,2,2,1,1,1,1] => [8,2,2,1,1,1,1]
[8,2,1,1,1,1,1,1] => [6,2,2,1,1,1,1,1,1]
[8,1,1,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1]
[7,7,2] => [6,4,3,2,1]
[7,7,1,1] => [4,4,3,2,1,1,1]
[7,6,3] => [5,4,4,3]
[7,6,2,1] => [6,4,3,3]
[7,6,1,1,1] => [6,5,2,1,1,1]
[7,5,4] => [6,5,2,2,1]
[7,5,3,1] => [4,3,3,2,2,1,1]
[7,5,2,2] => [8,3,2,2,1]
[7,5,2,1,1] => [4,4,3,3,1,1]
[7,5,1,1,1,1] => [4,3,2,2,1,1,1,1,1]
[7,4,4,1] => [6,5,3,2]
[7,4,3,2] => [7,4,3,2]
[7,4,3,1,1] => [5,4,4,1,1,1]
[7,4,2,2,1] => [8,3,3,2]
[7,4,2,1,1,1] => [7,4,2,1,1,1]
[7,4,1,1,1,1,1] => [5,4,2,1,1,1,1,1]
[7,3,3,3] => [3,3,3,2,2,2,1]
[7,3,3,2,1] => [3,3,3,3,2,2]
[7,3,3,1,1,1] => [3,3,2,2,2,1,1,1,1]
[7,3,2,2,2] => [9,2,2,2,1]
[7,3,2,2,1,1] => [6,4,3,1,1,1]
[7,3,2,1,1,1,1] => [4,4,3,1,1,1,1,1]
[7,3,1,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1,1,1]
[7,2,2,2,2,1] => [9,3,2,2]
[7,2,2,2,1,1,1] => [8,4,1,1,1,1]
[7,2,2,1,1,1,1,1] => [6,4,1,1,1,1,1,1]
[7,2,1,1,1,1,1,1,1] => [4,4,1,1,1,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1,1]
[6,6,4] => [6,6,4]
[6,6,3,1] => [6,6,3,1]
[6,6,2,2] => [8,4,4]
[6,6,2,1,1] => [8,4,3,1]
[6,6,1,1,1,1] => [8,3,2,1,1,1]
[6,5,5] => [6,5,4,1]
[6,5,4,1] => [6,5,5]
[6,5,3,2] => [7,4,4,1]
[6,5,3,1,1] => [6,3,3,2,1,1]
[6,5,2,2,1] => [7,5,4]
[6,5,2,1,1,1] => [7,6,1,1,1]
[6,5,1,1,1,1,1] => [6,3,2,1,1,1,1,1]
[6,4,4,2] => [8,6,2]
[6,4,4,1,1] => [8,6,1,1]
[6,4,3,3] => [7,6,2,1]
[6,4,3,2,1] => [7,7,2]
[6,4,3,1,1,1] => [7,3,2,2,1,1]
[6,4,2,2,2] => [10,4,2]
[6,4,2,2,1,1] => [10,4,1,1]
[6,4,2,1,1,1,1] => [9,2,2,1,1,1]
[6,4,1,1,1,1,1,1] => [7,2,2,1,1,1,1,1]
[6,3,3,3,1] => [5,5,2,2,1,1]
[6,3,3,2,2] => [9,4,2,1]
[6,3,3,2,1,1] => [6,5,3,1,1]
[6,3,3,1,1,1,1] => [5,3,2,2,1,1,1,1]
[6,3,2,2,2,1] => [9,5,2]
[6,3,2,2,1,1,1] => [8,5,1,1,1]
[6,3,2,1,1,1,1,1] => [6,5,1,1,1,1,1]
[6,3,1,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1,1]
[6,2,2,2,2,2] => [12,2,2]
[6,2,2,2,2,1,1] => [12,2,1,1]
[6,2,2,2,1,1,1,1] => [10,2,1,1,1,1]
[6,2,2,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1]
[6,2,1,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1]
[5,5,5,1] => [5,4,3,2,1,1]
[5,5,4,2] => [8,5,2,1]
[5,5,4,1,1] => [5,4,3,3,1]
[5,5,3,3] => [4,3,3,3,2,1]
[5,5,3,2,1] => [4,3,3,3,3]
[5,5,3,1,1,1] => [4,3,3,2,1,1,1,1]
[5,5,2,2,2] => [10,3,2,1]
[5,5,2,2,1,1] => [6,3,3,3,1]
[5,5,2,1,1,1,1] => [5,4,3,1,1,1,1]
[5,5,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1,1]
[5,4,4,3] => [7,6,3]
[5,4,4,2,1] => [8,5,3]
[5,4,4,1,1,1] => [7,4,3,1,1]
[5,4,3,3,1] => [5,5,4,1,1]
[5,4,3,2,2] => [9,4,3]
[5,4,3,2,1,1] => [5,5,5,1]
[5,4,3,1,1,1,1] => [5,5,2,1,1,1,1]
[5,4,2,2,2,1] => [10,3,3]
[5,4,2,2,1,1,1] => [9,4,1,1,1]
[5,4,2,1,1,1,1,1] => [7,4,1,1,1,1,1]
[5,4,1,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1,1]
[5,3,3,3,2] => [5,3,3,2,2,1]
[5,3,3,3,1,1] => [3,3,3,2,2,1,1,1]
[5,3,3,2,2,1] => [5,3,3,3,2]
[5,3,3,2,1,1,1] => [4,3,3,3,1,1,1]
[5,3,3,1,1,1,1,1] => [3,3,2,2,1,1,1,1,1,1]
[5,3,2,2,2,2] => [11,2,2,1]
[5,3,2,2,2,1,1] => [8,3,3,1,1]
[5,3,2,2,1,1,1,1] => [6,3,3,1,1,1,1]
[5,3,2,1,1,1,1,1,1] => [4,3,3,1,1,1,1,1,1]
[5,3,1,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1,1,1]
[5,2,2,2,2,2,1] => [11,3,2]
[5,2,2,2,2,1,1,1] => [10,3,1,1,1]
[5,2,2,2,1,1,1,1,1] => [8,3,1,1,1,1,1]
[5,2,2,1,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1,1]
[5,2,1,1,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1]
[4,4,4,4] => [8,8]
[4,4,4,3,1] => [8,7,1]
[4,4,4,2,2] => [10,6]
[4,4,4,2,1,1] => [10,5,1]
[4,4,4,1,1,1,1] => [9,3,2,1,1]
[4,4,3,3,2] => [9,6,1]
[4,4,3,3,1,1] => [7,5,2,1,1]
[4,4,3,2,2,1] => [9,7]
[4,4,3,2,1,1,1] => [7,7,1,1]
[4,4,3,1,1,1,1,1] => [7,3,2,1,1,1,1]
[4,4,2,2,2,2] => [12,4]
[4,4,2,2,2,1,1] => [12,3,1]
[4,4,2,2,1,1,1,1] => [11,2,1,1,1]
[4,4,2,1,1,1,1,1,1] => [9,2,1,1,1,1,1]
[4,4,1,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1]
[4,3,3,3,3] => [5,5,3,2,1]
[4,3,3,3,2,1] => [5,5,3,3]
[4,3,3,3,1,1,1] => [5,3,3,2,1,1,1]
[4,3,3,2,2,2] => [11,4,1]
[4,3,3,2,2,1,1] => [7,5,3,1]
[4,3,3,2,1,1,1,1] => [5,5,3,1,1,1]
[4,3,3,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1]
[4,3,2,2,2,2,1] => [11,5]
[4,3,2,2,2,1,1,1] => [9,5,1,1]
[4,3,2,2,1,1,1,1,1] => [7,5,1,1,1,1]
[4,3,2,1,1,1,1,1,1,1] => [5,5,1,1,1,1,1,1]
[4,3,1,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1]
[4,2,2,2,2,2,2] => [14,2]
[4,2,2,2,2,2,1,1] => [14,1,1]
[4,2,2,2,2,1,1,1,1] => [12,1,1,1,1]
[4,2,2,2,1,1,1,1,1,1] => [10,1,1,1,1,1,1]
[4,2,2,1,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1]
[3,3,3,3,3,1] => [3,3,3,3,2,1,1]
[3,3,3,3,2,2] => [7,3,3,2,1]
[3,3,3,3,2,1,1] => [3,3,3,3,3,1]
[3,3,3,3,1,1,1,1] => [3,3,3,2,1,1,1,1,1]
[3,3,3,2,2,2,1] => [7,3,3,3]
[3,3,3,2,2,1,1,1] => [5,3,3,3,1,1]
[3,3,3,2,1,1,1,1,1] => [3,3,3,3,1,1,1,1]
[3,3,3,1,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1,1,1]
[3,3,2,2,2,2,2] => [13,2,1]
[3,3,2,2,2,2,1,1] => [9,3,3,1]
[3,3,2,2,2,1,1,1,1] => [7,3,3,1,1,1]
[3,3,2,2,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1]
[3,3,2,1,1,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2,2,1] => [13,3]
[3,2,2,2,2,2,1,1,1] => [11,3,1,1]
[3,2,2,2,2,1,1,1,1,1] => [9,3,1,1,1,1]
[3,2,2,2,1,1,1,1,1,1,1] => [7,3,1,1,1,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1]
[3,2,1,1,1,1,1,1,1,1,1,1,1] => [3,3,1,1,1,1,1,1,1,1,1,1]
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[2,2,2,2,2,2,2,2] => [16]
[2,2,2,2,2,2,2,1,1] => [15,1]
[2,2,2,2,2,2,1,1,1,1] => [13,1,1,1]
[2,2,2,2,2,1,1,1,1,1,1] => [11,1,1,1,1,1]
[2,2,2,2,1,1,1,1,1,1,1,1] => [9,1,1,1,1,1,1,1]
[2,2,2,1,1,1,1,1,1,1,1,1,1] => [7,1,1,1,1,1,1,1,1,1]
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => [5,1,1,1,1,1,1,1,1,1,1,1]
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
[17] => [2,2,2,2,2,2,2,2,1]
[16,1] => [3,2,2,2,2,2,2,2]
[15,2] => [4,2,2,2,2,2,2,1]
[15,1,1] => [2,2,2,2,2,2,2,1,1,1]
[14,3] => [4,3,2,2,2,2,2]
[14,2,1] => [5,2,2,2,2,2,2]
[14,1,1,1] => [4,2,2,2,2,2,1,1,1]
[13,4] => [4,4,2,2,2,2,1]
[13,3,1] => [3,2,2,2,2,2,2,1,1]
[13,2,2] => [6,2,2,2,2,2,1]
[13,2,1,1] => [4,4,2,2,2,1,1,1]
[13,1,1,1,1] => [2,2,2,2,2,2,1,1,1,1,1]
[12,5] => [4,4,3,2,2,2]
[12,4,1] => [5,4,2,2,2,2]
[12,3,2] => [6,3,2,2,2,2]
[12,3,1,1] => [5,2,2,2,2,2,1,1]
[12,2,2,1] => [7,2,2,2,2,2]
[12,2,1,1,1] => [6,2,2,2,2,1,1,1]
[12,1,1,1,1,1] => [4,2,2,2,2,1,1,1,1,1]
[11,6] => [4,4,4,2,2,1]
[11,5,1] => [4,3,2,2,2,2,1,1]
[11,4,2] => [6,4,2,2,2,1]
[11,4,1,1] => [4,4,4,2,1,1,1]
[11,3,3] => [3,3,2,2,2,2,2,1]
[11,3,2,1] => [3,3,3,2,2,2,2]
[11,3,1,1,1] => [3,2,2,2,2,2,1,1,1,1]
[11,2,2,2] => [8,2,2,2,2,1]
[11,2,2,1,1] => [6,4,2,2,1,1,1]
[11,2,1,1,1,1] => [4,4,2,2,1,1,1,1,1]
[11,1,1,1,1,1,1] => [2,2,2,2,2,1,1,1,1,1,1,1]
[10,7] => [4,4,4,3,2]
[10,6,1] => [5,4,4,2,2]
[10,5,2] => [6,4,3,2,2]
[10,5,1,1] => [6,3,2,2,2,1,1]
[10,4,3] => [6,5,2,2,2]
[10,4,2,1] => [7,4,2,2,2]
[10,4,1,1,1] => [7,2,2,2,2,1,1]
[10,3,3,1] => [5,4,2,2,2,1,1]
[10,3,2,2] => [8,3,2,2,2]
[10,3,2,1,1] => [6,6,2,1,1,1]
[10,3,1,1,1,1] => [5,2,2,2,2,1,1,1,1]
[10,2,2,2,1] => [9,2,2,2,2]
[10,2,2,1,1,1] => [8,2,2,2,1,1,1]
[10,2,1,1,1,1,1] => [6,2,2,2,1,1,1,1,1]
[10,1,1,1,1,1,1,1] => [4,2,2,2,1,1,1,1,1,1,1]
[9,8] => [4,4,4,4,1]
[9,7,1] => [4,4,3,2,2,1,1]
[9,6,2] => [6,4,4,2,1]
[9,6,1,1] => [4,4,4,3,1,1]
[9,5,3] => [4,3,3,2,2,2,1]
[9,5,2,1] => [4,3,3,3,2,2]
[9,5,1,1,1] => [4,3,2,2,2,1,1,1,1]
[9,4,4] => [6,6,2,2,1]
[9,4,3,1] => [5,4,4,2,1,1]
[9,4,2,2] => [8,4,2,2,1]
[9,4,2,1,1] => [6,4,4,1,1,1]
[9,4,1,1,1,1] => [5,4,2,2,1,1,1,1]
[9,3,3,2] => [5,3,2,2,2,2,1]
[9,3,3,1,1] => [3,3,2,2,2,2,1,1,1]
[9,3,2,2,1] => [5,3,3,2,2,2]
[9,3,2,1,1,1] => [4,4,4,1,1,1,1,1]
[9,3,1,1,1,1,1] => [3,2,2,2,2,1,1,1,1,1,1]
[9,2,2,2,2] => [10,2,2,2,1]
[9,2,2,2,1,1] => [8,4,2,1,1,1]
[9,2,2,1,1,1,1] => [6,4,2,1,1,1,1,1]
[9,2,1,1,1,1,1,1] => [4,4,2,1,1,1,1,1,1,1]
[9,1,1,1,1,1,1,1,1] => [2,2,2,2,1,1,1,1,1,1,1,1,1]
[8,8,1] => [5,4,4,4]
[8,7,2] => [6,4,4,3]
[8,7,1,1] => [6,4,3,2,1,1]
[8,6,3] => [6,5,4,2]
[8,6,2,1] => [7,4,4,2]
[8,6,1,1,1] => [8,3,2,2,1,1]
[8,5,4] => [6,6,3,2]
[8,5,3,1] => [6,5,2,2,1,1]
[8,5,2,2] => [8,4,3,2]
[8,5,2,1,1] => [6,6,3,1,1]
[8,5,1,1,1,1] => [6,3,2,2,1,1,1,1]
[8,4,4,1] => [7,6,2,2]
[8,4,3,2] => [8,5,2,2]
[8,4,3,1,1] => [7,4,2,2,1,1]
[8,4,2,2,1] => [9,4,2,2]
[8,4,2,1,1,1] => [9,2,2,2,1,1]
[8,4,1,1,1,1,1] => [7,2,2,2,1,1,1,1]
[8,3,3,3] => [5,5,2,2,2,1]
[8,3,3,2,1] => [5,5,3,2,2]
[8,3,3,1,1,1] => [5,3,2,2,2,1,1,1]
[8,3,2,2,2] => [10,3,2,2]
[8,3,2,2,1,1] => [8,6,1,1,1]
[8,3,2,1,1,1,1] => [6,6,1,1,1,1,1]
[8,3,1,1,1,1,1,1] => [5,2,2,2,1,1,1,1,1,1]
[8,2,2,2,2,1] => [11,2,2,2]
[8,2,2,2,1,1,1] => [10,2,2,1,1,1]
[8,2,2,1,1,1,1,1] => [8,2,2,1,1,1,1,1]
[8,2,1,1,1,1,1,1,1] => [6,2,2,1,1,1,1,1,1,1]
[8,1,1,1,1,1,1,1,1,1] => [4,2,2,1,1,1,1,1,1,1,1,1]
[7,7,3] => [4,4,3,3,2,1]
[7,7,2,1] => [4,4,3,3,3]
[7,7,1,1,1] => [4,4,3,2,1,1,1,1]
[7,6,4] => [6,6,4,1]
[7,6,3,1] => [5,4,4,3,1]
[7,6,2,2] => [8,4,4,1]
[7,6,2,1,1] => [6,4,3,3,1]
[7,6,1,1,1,1] => [6,5,2,1,1,1,1]
[7,5,5] => [5,4,3,2,2,1]
[7,5,4,1] => [5,4,3,3,2]
[7,5,3,2] => [6,3,3,2,2,1]
[7,5,3,1,1] => [4,3,3,2,2,1,1,1]
[7,5,2,2,1] => [6,3,3,3,2]
[7,5,2,1,1,1] => [5,4,4,1,1,1,1]
[7,5,1,1,1,1,1] => [4,3,2,2,1,1,1,1,1,1]
[7,4,4,2] => [8,6,2,1]
[7,4,4,1,1] => [7,4,4,1,1]
[7,4,3,3] => [5,5,4,2,1]
[7,4,3,2,1] => [5,5,5,2]
[7,4,3,1,1,1] => [5,5,2,2,1,1,1]
[7,4,2,2,2] => [10,4,2,1]
[7,4,2,2,1,1] => [8,4,3,1,1]
[7,4,2,1,1,1,1] => [7,4,2,1,1,1,1]
[7,4,1,1,1,1,1,1] => [5,4,2,1,1,1,1,1,1]
[7,3,3,3,1] => [3,3,3,2,2,2,1,1]
[7,3,3,2,2] => [7,3,2,2,2,1]
[7,3,3,2,1,1] => [4,4,3,3,1,1,1]
[7,3,3,1,1,1,1] => [3,3,2,2,2,1,1,1,1,1]
[7,3,2,2,2,1] => [7,3,3,2,2]
[7,3,2,2,1,1,1] => [6,4,3,1,1,1,1]
[7,3,2,1,1,1,1,1] => [4,4,3,1,1,1,1,1,1]
[7,3,1,1,1,1,1,1,1] => [3,2,2,2,1,1,1,1,1,1,1,1]
[7,2,2,2,2,2] => [12,2,2,1]
[7,2,2,2,2,1,1] => [10,4,1,1,1]
[7,2,2,2,1,1,1,1] => [8,4,1,1,1,1,1]
[7,2,2,1,1,1,1,1,1] => [6,4,1,1,1,1,1,1,1]
[7,2,1,1,1,1,1,1,1,1] => [4,4,1,1,1,1,1,1,1,1,1]
[7,1,1,1,1,1,1,1,1,1,1] => [2,2,2,1,1,1,1,1,1,1,1,1,1,1]
[6,6,5] => [6,6,5]
[6,6,4,1] => [7,6,4]
[6,6,3,2] => [8,5,4]
[6,6,3,1,1] => [8,5,2,1,1]
[6,6,2,2,1] => [9,4,4]
[6,6,2,1,1,1] => [10,3,2,1,1]
[6,6,1,1,1,1,1] => [8,3,2,1,1,1,1]
[6,5,5,1] => [6,5,4,1,1]
[6,5,4,2] => [8,6,3]
[6,5,4,1,1] => [6,5,5,1]
[6,5,3,3] => [6,5,3,2,1]
[6,5,3,2,1] => [6,5,3,3]
[6,5,3,1,1,1] => [6,3,3,2,1,1,1]
[6,5,2,2,2] => [10,4,3]
[6,5,2,2,1,1] => [8,5,3,1]
[6,5,2,1,1,1,1] => [7,6,1,1,1,1]
[6,5,1,1,1,1,1,1] => [6,3,2,1,1,1,1,1,1]
[6,4,4,3] => [8,7,2]
[6,4,4,2,1] => [9,6,2]
[6,4,4,1,1,1] => [9,4,2,1,1]
[6,4,3,3,1] => [7,6,2,1,1]
[6,4,3,2,2] => [10,5,2]
[6,4,3,2,1,1] => [8,7,1,1]
[6,4,3,1,1,1,1] => [7,3,2,2,1,1,1]
[6,4,2,2,2,1] => [11,4,2]
[6,4,2,2,1,1,1] => [11,2,2,1,1]
[6,4,2,1,1,1,1,1] => [9,2,2,1,1,1,1]
[6,4,1,1,1,1,1,1,1] => [7,2,2,1,1,1,1,1,1]
[6,3,3,3,2] => [7,5,2,2,1]
[6,3,3,3,1,1] => [5,3,3,2,2,1,1]
[6,3,3,2,2,1] => [7,5,3,2]
[6,3,3,2,1,1,1] => [6,5,3,1,1,1]
[6,3,3,1,1,1,1,1] => [5,3,2,2,1,1,1,1,1]
[6,3,2,2,2,2] => [12,3,2]
[6,3,2,2,2,1,1] => [10,5,1,1]
[6,3,2,2,1,1,1,1] => [8,5,1,1,1,1]
[6,3,2,1,1,1,1,1,1] => [6,5,1,1,1,1,1,1]
[6,3,1,1,1,1,1,1,1,1] => [5,2,2,1,1,1,1,1,1,1,1]
[6,2,2,2,2,2,1] => [13,2,2]
[6,2,2,2,2,1,1,1] => [12,2,1,1,1]
[6,2,2,2,1,1,1,1,1] => [10,2,1,1,1,1,1]
[6,2,2,1,1,1,1,1,1,1] => [8,2,1,1,1,1,1,1,1]
[6,2,1,1,1,1,1,1,1,1,1] => [6,2,1,1,1,1,1,1,1,1,1]
[6,1,1,1,1,1,1,1,1,1,1,1] => [4,2,1,1,1,1,1,1,1,1,1,1,1]
[5,5,5,2] => [7,4,3,2,1]
[5,5,5,1,1] => [5,4,3,2,1,1,1]
[5,5,4,3] => [5,5,4,3]
[5,5,4,2,1] => [7,4,3,3]
[5,5,4,1,1,1] => [5,4,3,3,1,1]
[5,5,3,3,1] => [4,3,3,3,2,1,1]
[5,5,3,2,2] => [8,3,3,2,1]
[5,5,3,2,1,1] => [4,3,3,3,3,1]
[5,5,3,1,1,1,1] => [4,3,3,2,1,1,1,1,1]
[5,5,2,2,2,1] => [8,3,3,3]
[5,5,2,2,1,1,1] => [7,4,3,1,1,1]
[5,5,2,1,1,1,1,1] => [5,4,3,1,1,1,1,1]
[5,5,1,1,1,1,1,1,1] => [4,3,2,1,1,1,1,1,1,1,1]
[5,4,4,4] => [8,8,1]
[5,4,4,3,1] => [7,6,3,1]
[5,4,4,2,2] => [10,6,1]
[5,4,4,2,1,1] => [9,4,3,1]
[5,4,4,1,1,1,1] => [7,5,2,1,1,1]
[5,4,3,3,2] => [7,5,4,1]
[5,4,3,3,1,1] => [5,5,4,1,1,1]
[5,4,3,2,2,1] => [7,5,5]
[5,4,3,2,1,1,1] => [5,5,5,1,1]
[5,4,3,1,1,1,1,1] => [5,5,2,1,1,1,1,1]
[5,4,2,2,2,2] => [12,4,1]
[5,4,2,2,2,1,1] => [10,3,3,1]
[5,4,2,2,1,1,1,1] => [9,4,1,1,1,1]
[5,4,2,1,1,1,1,1,1] => [7,4,1,1,1,1,1,1]
[5,4,1,1,1,1,1,1,1,1] => [5,4,1,1,1,1,1,1,1,1]
[5,3,3,3,3] => [3,3,3,3,2,2,1]
[5,3,3,3,2,1] => [3,3,3,3,3,2]
[5,3,3,3,1,1,1] => [3,3,3,2,2,1,1,1,1]
[5,3,3,2,2,2] => [9,3,2,2,1]
[5,3,3,2,2,1,1] => [6,3,3,3,1,1]
[5,3,3,2,1,1,1,1] => [4,3,3,3,1,1,1,1]
[5,3,3,1,1,1,1,1,1] => [3,3,2,2,1,1,1,1,1,1,1]
[5,3,2,2,2,2,1] => [9,3,3,2]
[5,3,2,2,2,1,1,1] => [8,3,3,1,1,1]
[5,3,2,2,1,1,1,1,1] => [6,3,3,1,1,1,1,1]
[5,3,2,1,1,1,1,1,1,1] => [4,3,3,1,1,1,1,1,1,1]
[5,3,1,1,1,1,1,1,1,1,1] => [3,2,2,1,1,1,1,1,1,1,1,1,1]
[5,2,2,2,2,2,2] => [14,2,1]
[5,2,2,2,2,2,1,1] => [12,3,1,1]
[5,2,2,2,2,1,1,1,1] => [10,3,1,1,1,1]
[5,2,2,2,1,1,1,1,1,1] => [8,3,1,1,1,1,1,1]
[5,2,2,1,1,1,1,1,1,1,1] => [6,3,1,1,1,1,1,1,1,1]
[5,2,1,1,1,1,1,1,1,1,1,1] => [4,3,1,1,1,1,1,1,1,1,1,1]
[5,1,1,1,1,1,1,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]
[4,4,4,4,1] => [9,8]
[4,4,4,3,2] => [10,7]
[4,4,4,3,1,1] => [9,6,1,1]
[4,4,4,2,2,1] => [11,6]
[4,4,4,2,1,1,1] => [11,4,1,1]
[4,4,4,1,1,1,1,1] => [9,3,2,1,1,1]
[4,4,3,3,3] => [7,7,2,1]
[4,4,3,3,2,1] => [7,7,3]
[4,4,3,3,1,1,1] => [7,3,3,2,1,1]
[4,4,3,2,2,2] => [12,5]
[4,4,3,2,2,1,1] => [9,7,1]
[4,4,3,2,1,1,1,1] => [7,7,1,1,1]
[4,4,3,1,1,1,1,1,1] => [7,3,2,1,1,1,1,1]
[4,4,2,2,2,2,1] => [13,4]
[4,4,2,2,2,1,1,1] => [13,2,1,1]
[4,4,2,2,1,1,1,1,1] => [11,2,1,1,1,1]
[4,4,2,1,1,1,1,1,1,1] => [9,2,1,1,1,1,1,1]
[4,4,1,1,1,1,1,1,1,1,1] => [7,2,1,1,1,1,1,1,1,1]
[4,3,3,3,3,1] => [5,5,3,2,1,1]
[4,3,3,3,2,2] => [9,5,2,1]
[4,3,3,3,2,1,1] => [5,5,3,3,1]
[4,3,3,3,1,1,1,1] => [5,3,3,2,1,1,1,1]
[4,3,3,2,2,2,1] => [9,5,3]
[4,3,3,2,2,1,1,1] => [7,5,3,1,1]
[4,3,3,2,1,1,1,1,1] => [5,5,3,1,1,1,1]
[4,3,3,1,1,1,1,1,1,1] => [5,3,2,1,1,1,1,1,1,1]
[4,3,2,2,2,2,2] => [14,3]
[4,3,2,2,2,2,1,1] => [11,5,1]
[4,3,2,2,2,1,1,1,1] => [9,5,1,1,1]
[4,3,2,2,1,1,1,1,1,1] => [7,5,1,1,1,1,1]
[4,3,2,1,1,1,1,1,1,1,1] => [5,5,1,1,1,1,1,1,1]
[4,3,1,1,1,1,1,1,1,1,1,1] => [5,2,1,1,1,1,1,1,1,1,1,1]
[4,2,2,2,2,2,2,1] => [15,2]
[4,2,2,2,2,2,1,1,1] => [14,1,1,1]
[4,2,2,2,2,1,1,1,1,1] => [12,1,1,1,1,1]
[4,2,2,2,1,1,1,1,1,1,1] => [10,1,1,1,1,1,1,1]
[4,2,2,1,1,1,1,1,1,1,1,1] => [8,1,1,1,1,1,1,1,1,1]
[4,2,1,1,1,1,1,1,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1,1,1,1]
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => [4,1,1,1,1,1,1,1,1,1,1,1,1,1]
[3,3,3,3,3,2] => [5,3,3,3,2,1]
[3,3,3,3,3,1,1] => [3,3,3,3,2,1,1,1]
[3,3,3,3,2,2,1] => [5,3,3,3,3]
[3,3,3,3,2,1,1,1] => [3,3,3,3,3,1,1]
[3,3,3,3,1,1,1,1,1] => [3,3,3,2,1,1,1,1,1,1]
[3,3,3,2,2,2,2] => [11,3,2,1]
[3,3,3,2,2,2,1,1] => [7,3,3,3,1]
[3,3,3,2,2,1,1,1,1] => [5,3,3,3,1,1,1]
[3,3,3,2,1,1,1,1,1,1] => [3,3,3,3,1,1,1,1,1]
[3,3,3,1,1,1,1,1,1,1,1] => [3,3,2,1,1,1,1,1,1,1,1,1]
[3,3,2,2,2,2,2,1] => [11,3,3]
[3,3,2,2,2,2,1,1,1] => [9,3,3,1,1]
[3,3,2,2,2,1,1,1,1,1] => [7,3,3,1,1,1,1]
[3,3,2,2,1,1,1,1,1,1,1] => [5,3,3,1,1,1,1,1,1]
[3,3,2,1,1,1,1,1,1,1,1,1] => [3,3,3,1,1,1,1,1,1,1,1]
[3,3,1,1,1,1,1,1,1,1,1,1,1] => [3,2,1,1,1,1,1,1,1,1,1,1,1,1]
[3,2,2,2,2,2,2,2] => [16,1]
[3,2,2,2,2,2,2,1,1] => [13,3,1]
[3,2,2,2,2,2,1,1,1,1] => [11,3,1,1,1]
[3,2,2,2,2,1,1,1,1,1,1] => [9,3,1,1,1,1,1]
[3,2,2,2,1,1,1,1,1,1,1,1] => [7,3,1,1,1,1,1,1,1]
[3,2,2,1,1,1,1,1,1,1,1,1,1] => [5,3,1,1,1,1,1,1,1,1,1]
-----------------------------------------------------------------------------
Created: Jan 29, 2024 at 14:51 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Oct 15, 2024 at 03:00 by Nadia Lafreniere